1. Scope of the invention
The invention relates to a digital filter device to which a digital signal is applied which is transformed into a digital output signal in a predetermined manner. Such a filter device may be intended to limit the frequency band of the input signal and may be designed so as to form, for example, a low-pass filter, a band-pass filter or a band-stop filter, or a high-pass filter. The said digital filter devices can in general be divided into two classes which denote the manner of realizing the filter, viz. recursive filters and non-recursive filters. Hereinafter instead of the term "digital filter device" the term "digital filter" will be used.
2. Description of the state of the art
The digital signal which is applied to the digital filter in general is constituted by a sequence of binary-coded numbers which hereinafter will be represented by x(nT). These binary-coded numbers which each comprise a plurality of binary digits (bits) in general represent samples of an analog information signal. These numbers are obtained by sampling the analog information signal in the usual manner at a fixed sampling frequency 1/T and quantizing the resulting time-discrete signal values and representing them in a binary code. In this connection the term "time-discrete" means that signal samples are taken at discrete instants nT, where n = 0, 1, 2, . . . represents the number of samples which have been taken after the instant t = 0, which samplings occur with a sampling period T.
The transformation of these binary-coded numbers x(nT) in the digital filter consists in that they are subjected to a predetermined sequence of arithmetic operations, resulting in binary-coded numbers which are delivered by the filter as digital output signals. If, as frequently is the case, after insertion of a binary-coded number x(nT) the filter delivers only one single binary-coded output number, these output numbers of the filter can be represented by y(nT).
If the filter is arranged, for example, to limit the frequency band of the analog information signal, for a recursive digital filter the operation to be performed can mathematically be represented by: ##EQU1## AND FOR A NON-RECURSIVE DIGITAL FILTER BY: ##EQU2##
In these expressions the likewise binary-coded numbers a.sub.k, b.sub.k and h(kT) are referred to as filter coefficients, and these coefficients are determined by the transfer function of the filter. The number h(kT) more particularly represent the binary-coded samples of the impulse response of the digital filter, which impulse response isalso sampled at a frequency of 1/T.
It should be mentioned that the expression (1) represents a recursive digital filter of the Mth order and that the non-recursive filter represented by the expression (2) belongs in the class of FIR (finite impulse response) filters.
For performing the operations given by the expressions (1) and (2) on the numbers x(nT) the digital filter in general includes storing means in which the successively occurring numbers x(nT) are stored. This storing means may, for example, be in the form of a shift register into each shift register element of which a number x(nT) can be stored. The filter further includes a multiplying device to which the stored numbers x(nT) and the respective filter coefficients a.sub.k and h(kT) are supplied for forming binary-coded numbers which represent the various products a.sub.k x (n - k)T and h(kT).x [(n - k)T]. These products are supplied to an adding-device in which they are added to one another. As follows from expression (1), for the recursive digital filter this operation is also and identically performed on a given number of M output numbers y [(n - k)T] which immediately precede the output number y(nT) to be determined.
A usual method of performing a multiplication, for example h(kT). x [(n - k) T], consists in that each time one bit of the coefficient h(kT) is multiplied by the multiplicand x [(n - k)T]. The obtained partial products, which are equal either to zero or to the multiplicand, are accumulated in an accumulator after being shifted a number of places equal to the magnitude of the exponent of the relevant bit of the coefficent.
If generating a partial product in conjunction with adding the shifted partial product in the accumulator is defined to as an elementary operation, the number of elementary operations for performing a complete multiplication is equal to the number of bits of the filter coefficient (for example h(kT) ) increased by one. Each of these elementary operations is performed under the control of a clock pulse generator which for this purpose generates clock pulses at a frequency f.sub.p which is proportional both to the sampling frequency 1/T and to the number of bits of which each filter coefficient consists. If, for example, the expression (2) is realized by serial processing, this frequency f.sub.p is also proportional to the number of input numbers x(nT) required to determine an output number y(nT).
Because the components used set a limit to the maximum value of the said frequency f.sub.p, a limit is set to the number of bits from which the numbers x(nT), y(nT), a.sub.k, b.sub.k, h(kT) are built up and, in the case of serial performance of expression (2), also to the number of numbers x(nT) which can be taken into consideration for determining an output number y(nT).
However, it is just the aforementioned factors which determine the accuracy with which a desired transfer characteristic can be realized.
It is an object of the present invention to provide a digital filter which enables the frequency f.sub.p of the clock pulse generator to be considerably reduced and which is highly flexible and capable of universal application.